Question

3a 5кг яблок и 4кг груш заплатили 10грн. Известно, что 3кг яблок стоят дороже 2кг груш на 1,6грн. Сколько стоит 1 кг яблок и 1 кг груш?​

Answer 1

Ответ:

1,2гр стоит 1 кг яблок и 1гр  стоит 1 кг груш

Пошаговое объяснение:

х - стоят яблоки

у- стоят груши, составим систему уравнений:

$\left \{ {{5x+4y=10}\atop{3x-2y=1,6}} \right.$ разделим обе части первого уравнения на 5:

$\left \{ {{x+0,8y=2}\atop{3x-2y=1,6}} \right.$

$\left \{ {{x=2-0,8y}\atop{3x-2y=1,6}} \right.$ подставим значение х, во 2е уравнение:

3*(2-0,8у)-2у=1,6

6-2,4у-2у=1,6

-4,4у=1,6-6

-4,4у=-4,4

у=-4,4:(-4,4)

у=1

х=2-0,8у

х=2-0,8*1

х=1,2

Answer 2

Problem Analysis

We are given that 3 kg of apples and 4 kg of pears were purchased for a total of 10 UAH. Additionally, we know that 3 kg of apples cost 1.6 UAH more than 2 kg of pears. We need to determine the cost of 1 kg of apples and 1 kg of pears.

Solution

Let's assume the cost of 1 kg of apples is x UAH and the cost of 1 kg of pears is y UAH.

From the given information, we can set up the following equations:

Equation 1: 3x + 4y = 10 (since 3 kg of apples and 4 kg of pears were purchased for a total of 10 UAH)

Equation 2: 3x = 2y + 1.6 (since 3 kg of apples cost 1.6 UAH more than 2 kg of pears)

To solve this system of equations, we can use substitution or elimination method. Let's use the substitution method.

From Equation 2, we can express x in terms of y:

3x = 2y + 1.6 x = (2y + 1.6) / 3

Substituting this value of x into Equation 1, we get:

3 * ((2y + 1.6) / 3) + 4y = 10 2y + 1.6 + 4y = 10 6y + 1.6 = 10 6y = 10 - 1.6 6y = 8.4 y = 8.4 / 6 y = 1.4

Now, substituting the value of y back into Equation 1, we can find the value of x:

3x + 4 * 1.4 = 10 3x + 5.6 = 10 3x = 10 - 5.6 3x = 4.4 x = 4.4 / 3 x = 1.4667

Therefore, the cost of 1 kg of apples is approximately 1.47 UAH and the cost of 1 kg of pears is 1.4 UAH.

Answer: The cost of 1 kg of apples is approximately 1.47 UAH and the cost of 1 kg of pears is 1.4 UAH.

Explanation

Based on the given information, we can set up a system of equations to solve for the cost of 1 kg of apples and 1 kg of pears. By substituting the value of one variable into the other equation, we can find the values of both variables. In this case, the cost of 1 kg of apples is approximately 1.47 UAH and the cost of 1 kg of pears is 1.4 UAH.